Use the following triangles to determine the trig ratios below. Simplify all fractions, rationalize and simplify all radicals, and convert all decimal answers to fractions.
Problem 1 :
Solution :
Problem 2 :
Solution :
sin F =OppositeHypotenuse=DEDF=71052=710×25=1450sin F=725cos D =AdjacentHypotenuse=DEDF=71052=710×25=1450cos D=725cos F =AdjacentHypotenuse=EFDF=12552=125×25cos F=2425
Problem 3 :
Solution :
sin H =OppositeHypotenuse=GIGH=2.17.5=2.17.5×1010=2175sin H=725cos G =AdjacentHypotenuse=GIGH=2.17.5=2.17.5×1010=2175cos G=725tan H =OppositeAdjacent=GIHI=2.17.2=2.17.2×1010=2172tan H =724
Problem 4 :
Solution :
sin J =OppositeHypotenuse=KLJL=39sin J =13cos L =AdjacentHypotenuse=KLJL=39cos L=13tan L =OppositeAdjacent=KJKL=623tan L=221
Problem 5 :
Solution :
sin M =OppositeHypotenuse=NOMO=651310=65×1013=6065sin M=1213cos O =AdjacentHypotenuse=NOMO=651310=65×1013=6065cos O =1213tan M =OppositeAdjacent=NOMN=6512=65×21=125tan M=125
Problem 6 :
Solution :
sin P =OppositeHypotenuse=RQPR=2451sin P=817tan P =OppositeAdjacent=RQPQ=2445tan P =815tan R =OppositeAdjacent=PQRQ=4524tan R =158
Problem 7 :
Solution :
sin S =OppositeHypotenuse=UTST=2250.11=2250.1 × 101 × 10=225110= 225×101=2025=45sin S =45sin T =OppositeHypotenuse=SUST=0.0610.11=0.06 × 1001 × 1000.1 × 101 × 10=6100110= 6100×101=60100sin T=35tan T =OppositeAdjacent=SUUT=0.061225=0.06 × 1001 × 100225=6100225= 6100×252=150200tan T=34
Problem 8 :
Solution :
cos V =AdjacentHypotenuse=WXVW=66123cos V=22cos W =AdjacentHypotenuse=WXVW=66123cos W=22tan W =OppositeAdjacent=VXWX=25466=93=33tan W=11